Attitude and position estimation from vector observations

This paper introduces three novel methods to evaluate attitude and position from vector observations using a vision-based technology camera. The first approach, called Linear Algebra Resection Approach (LARA), solves for attitude and position simultaneously and can be used in the lost-in-space case, when no approximate solution is available. The solution is shown to be the left eigenvector associated with the minimum singular value of a rectangular data matrix. The second and third approaches, called Attitude Free Approaches (AFA), recast the problem into a nonlinear system of equations in terms of the unknown position only. Two different methods are proposed to solve this nonlinear set of equations. The First AFA (FAFA) uses a least-square Newton-Raphson iterative procedure and is particularly suitable for the recursive case, while the Second AFA (SAFA) uses the toric resultant to eliminate two variables from the attitude-free system of nonlinear polynomial equations and a discretization of the Cauchy integral theorem to quickly isolate the solution. SAFA can be used either in the lost-in-space or in the recursive cases. Final numerical tests quantify the robustness of these methods in the case of measurements affected by noise.

Attitude and position estimation from vector observations Conference Paper